The first-level spell shadow weapon creates an illusionary weapon the caster can wield. Consequently, the weapon thereby produced may find itself subjected to all manner of hostile effects by enemies who believe the weapon to be real (those who don't aren't usually too scared of the 1 damage it might inflict). It's unclear from the spell description, however, what the hardness and hp should be. How does one calculate that, and what are the values?
The spell shadow weapon allows the caster to create "a quasi-real masterwork melee weapon of a type you [i.e. the caster] are proficient with." Broadly, there are two choices.
1. The quasi-real weapon is composed of any material the caster desires therefore having hardness and hp appropriate to that material
The spell shadow weapon doesn't say the caster can't create a weapon that's composed of a special material, therefore when the caster casts the shadow weapon spell, the caster can create a masterwork dagger composed of adamantine or another special material with desirable effects, and the quasi-real weapon will have that hardness and hp appropriate to the material. The spell creates a quasi-real masterwork melee weapon with which the caster is proficient, and literally everything else about the weapon is up for grabs.
That is, it's possible to read the shadow weapon spell's silence as permission. The game doesn't specifically prevent the caster from creating a quasi-real weapon made from special materials, the caster can. Further, because the game doesn't specifically prevent the caster from creating a quasi-real masterwork weapon that's also magical, the caster can. With this reading in mind, when a caster casts the shadow weapon spell—that, by the way, is a 1st-level spell—the caster can opt to create a quasi-real +1 brilliant energy vorpal cold iron dagger.1
Then, when the caster is level 5, such a weapon's enhancement bonus could be increased by +1. And when level 10 such a weapon's enhancement bonus could instead be either increased by +2 or increased by +1 and the weapon would also gain the magic weapon special ability frost or keen.2
Using this reading, if the game wanted to forbid a level 1 character from bringing forth with the 1st-level spell shadow weapon a +1 brilliant energy vorpal cold iron dagger or whatever, the game should've added language to that effect. For example, instead of the shadow weapon spell description saying the spell creates a quasi-real masterwork melee weapon with which the caster is proficient, the spell description should've said that the spell creates a quasi-real otherwise nonmagical masterwork melee weapon that's composed of nonspecial material and with which the caster is proficient.3
Further, under this reading, every time the game introduces a new rules element involving weapons either the developers must step in and change the spell shadow weapon (which, so far as I'm aware, has remained untouched since its publication) or the spell's silence automatically permits those new weapon-based rules elements to be applied to a shadow weapon effect. For example weapon modifications are a thing, and, since the shadow weapon spell doesn't specifically exclude those, under this reading those are totally allowed, too.
Obviously, this reading makes the spell shadow weapon quite powerful. By extension, the word weapon wherever it's used in Pathfinder becomes loaded with meaning as it embraces the whole of the game's myriad weapons, from a broken Fine club to a +1 brilliant energy vorpal cold iron dagger to the Axe of the Dwarvish Lords.
2. The quasi-real weapon is composed of the default material for the picked weapon therefore the weapon has its normal hardness and hp
The spell shadow weapon doesn't say the caster can create a weapon that's composed of a special material, therefore the caster can't have the weapon that the spell creates be composed of a special material. Thus the quasi-real weapon defaults to its normal material and possesses the weapon's normal hardness and hp (see here).
That is, the spell's silence limits the spell. Because the shadow weapon spell doesn't specifically allow an effect, it's tacitly forbidding the effect. Under this reading, when the spell shadow weapon says "masterwork melee weapon" it means a melee weapon from the list of exotic, martial, and simple light, one-handed, and two-handed melee weapons here to which is added the masterwork component here. The spell must specify that magic weapon special abilities, the masterwork component, special materials, weapon modifications, and other effects are available, and the only one of those that the spell specifies initially is the masterwork component. The spell is already specific.
So, under this reading, in the same way that the shadow weapon spell doesn't allow the caster to fly or breathe fire, the spell also doesn't allow a caster to bring forth a quasi-real +1 brilliant energy vorpal cold iron dagger even though that is, in fact, a masterwork weapon with which the caster is proficient. Instead, assuming the caster's proficient, this reading allows the caster to bring forth just an otherwise normal masterwork dagger, and—to be extra clear—not a masterwork dagger composed of special materials.
1 Under the first reading, such a reader may wonder at the shadow weapon spell's inclusion of the word masterwork in the spell's description. The set weapons includes already the subset weapons possessing a masterwork component, after all.
2 Although a "single weapon cannot have a modified bonus (enhancement bonus plus special ability bonus equivalents, including those from character abilities and spells) higher than +10" (see here), this first reading could allow the shadow weapon spell's specific effect to beat this general rule.
3 The term otherwise nonmagical is necessary to eliminate the possibility of magical enhancement bonuses and magic weapon special abilities while still including the weapon itself that is a product of magic and possesses a magic aura.
There are no exact rules for this
Shadow Weapon is an Illusion (shadow) spell.
A shadow spell creates something that is partially real from extradimensional energy. Such illusions can have real effects. Damage dealt by a shadow illusion is real.
The form of the creation is not a conjuration and is instead made of energy, specifically from the Shadow Plane. How exactly it looks is between any given pairing of GM and player, but it is not Conjuration and therefor not actually physically there.
Other Shadow Illusions help make an educated choice
The physical characteristics of items are given as guidelines (and to cover the items that will most likely be damaged during adventuring), but ultimately it is up to the GM to decide the exact numbers that pertain in a given situation.
Shadow Structure* has
...5 hardness and 10 hit points for every 5 foot cube of the structure.
Shadow Terrain* specifically references Shadow Structure but increases this to
10 hardness and 20 hit points for every 5-ft.-cube of the structure.
My recommendation? Use the Hardness and HP of a one-handed hafted weapon (5/5, 7/15, or 9/25 depending on the enhancement bonus chosen). It should probably be a little more flimsy than metal/special material weapons, which is represented by the hafted weapons' lower Hardness.
*Note that these spells are 3rd party (Ascension Games) material. Depending on the GM, they may not be swayed by these numbers. Luckily, my personal recommendation is largely unrelated to them.